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Continuity at a boundary point of solutions to quasilinear elliptic equations with generalized Orlicz growth and non-logarithmic conditions
Oleksandr V. Hadzhy, Mykhailo V. Voitovych
We consider the Dirichlet problem for quasilinear elliptic equations with Musielak-Orlicz (p,q)-growth and non-logarithmic conditions on the coefficients. A sufficient Wiener-type…
On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions
Igor I. Skrypnik, Mykhailo V. Voitovych
We prove the continuity of bounded solutions for a wide class of parabolic equations with -growth $$ u_{t}-{\rm div}\left(g(x,t,|\nabla u|)\,\frac{\nabla u}{|\nabla u|}\righ…
Interior continuity, continuity up to the boundary and Harnack's inequality for double-phase elliptic equations with non-logarithmic conditions
Oleksandr V. Hadzhy, Igor I. Skrypnik, Mykhailo V. Voitovych
We prove continuity and Harnack's inequality for bounded solutions to elliptic equations of the type $$ \begin{aligned} {\rm div}\big(|\nabla u|^{p-2}\,\nabla u+a(x)|\nabla u|^{q-2…
Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth
M. A. Shan, I. I. Skrypnik, M. V. Voitovych
We prove Harnack's inequality for bounded weak solutions to quasilinear second order elliptic equations with generalized Orlicz growth conditions. Our approach covers new cases of…
classes of DeGiorgi-Ladyzhenskaya-Ural'tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions
Igor I. Skrypnik, Mykhailo V. Voitovych
We introduce elliptic and parabolic classes that generalize the well-known classes of DeGiorgi, Ladyzhenskaya and Ural'tseva with . New cl…